Question: Solve for $x$ and $y$ using elimination. ${5x-y = 28}$ ${-3x+y = -16}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $2x = 12$ $\dfrac{2x}{{2}} = \dfrac{12}{{2}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {5x-y = 28}\thinspace$ to find $y$ ${5}{(6)}{ - y = 28}$ $30-y = 28$ $30{-30} - y = 28{-30}$ $-y = -2$ $\dfrac{-y}{{-1}} = \dfrac{-2}{{-1}}$ ${y = 2}$ You can also plug ${x = 6}$ into $\thinspace {-3x+y = -16}\thinspace$ and get the same answer for $y$ : ${-3}{(6)}{ + y = -16}$ ${y = 2}$